2005 AMC 12A Problems/Problem 2

The following problem is from both the 2005 AMC 12A #2 and 2005 AMC 10A #3, so both problems redirect to this page.

Problem

The equations $2x + 7 = 3$ and $bx - 10 = -2$ have the same solution $x$ . What is the value of $b$ ?

$\mathrm {(A) } \ -8 \qquad \mathrm {(B) } \ -4 \qquad \mathrm {(C) } \ -2 \qquad \mathrm {(D) } \ 4 \qquad \mathrm {(E) } \ 8$

$2x + 7 = 3 \iff x = -2$ , so we require $-2b-10 = -2 \iff -2b = 8 \iff b = \boxed{\mathrm{(B) } \ -4}$ .

~Charles3829

2005 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

2005 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AMC 10 Problems and Solutions